基于等效加工时间模型的机床退化过程建模

doi:10.13229/j.cnki.jdxbgxb20211087

摘要/Abstract

摘要：

机床性能退化引起加工质量下降和其他问题，加工参数影响退化率。因为有多个加工参数，机床退化建模涉及多个变量，广泛使用的建模方法是回归分析。回归分析的主要缺点是精度依赖于所选平均退化函数，且不给出到退化限的时间分布。为克服上述问题，提出一个基于等效加工时间的建模方法，它将每个加工参数看作为一个“应力”，通过乘积模型组合多个加工参数成为一个“复合应力”；使用加速退化模型组合复合应力与实际加工时间成为一个等效加工时间，从而使多变量退化建模问题简化为单变量退化建模问题。最后，通过一个刀具磨损的实例例证了该方法的优越性。

关键词: 机床退化, 加工参数, 复合应力, 等效加工时间, 刀具磨损

Abstract:

Performance degradation of machine tools affects machining quality and causes other problems. Machining parameters affect the degradation rate. Since the number of machining parameters is often larger than one， the degradation modelling involves multiple variables. A popular modelling method is regression analysis， which has two drawbacks：（a） the accuracy depends on the chosen mean degradation function， and （b） it does not produce the distribution of time to degradation limit. To address these issues， this paper proposes an equivalent processing time based modelling method. The proposed method views each of machining parameters as a stress， uses the product model to combine the machining parameters into a composite stress， and use an accelerated degradation model to combine the composite stress and actual processing time into an equivalent processing time. In such a way， the multivariable degradation modelling problem is simplified into a univariate degradation modelling problem. A real-world example that deals with tool wear is included to illustrate the superiority of the proposed method.

Key words: degradation of machine tools, machining parameters, composite stress, equivalent processing time, tool wear

中图分类号:

TH17

蒋仁言,熊彬彬. 基于等效加工时间模型的机床退化过程建模[J]. 吉林大学学报(工学版), 2022, 52(2): 483-490.

Ren-yan JIANG,Bin-bin XIONG. Modelling degradation processes of machine tools using an equivalent processing time model[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 483-490.

图/表 9

表1

平均退化函数、形状及适用的磨损阶段"

名称	μ（z）	形状类型	磨损阶段
指数^［31］	$a (e b z - 1)$	凹的	拐点前
幂率^［31］	$(z / a) b$	凹的或凸的	拐点前
对数^［31］	$a l n (1 + z / b)$	凸的	拐点前
线性-指数^{［31，32］}	$a z + b (1 - e - c z)$	增或减且渐近常数	磨耗前
线性-对数	$a z + b l n (1 + c z)$	凸的渐近线性	磨耗前
线性-指数^［31-33］	$a z b e c z$	反S形的	全过程
对数幂率^［34］	$a [l n (1 + z / b)] c$	S形的	不适用

表1

表2

图1

表3

图2

表4

表5

表6

图3

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序号	V/（m·min^-1）	f/（mm·tooth^-1）	d/mm	y（t）/μm
序号	V/（m·min^-1）	f/（mm·tooth^-1）	d/mm	t=5	t=10	t=15	t=20	t=25
1	170	0.13	0.2	62	68	81	109	130
2	170	0.23	0.6	48	59	83	94	113
3	170	0.33	1.0	40	70	80	93	99
4	370	0.13	0.6	75	104	131	173	237
5	370	0.23	1.0	75	92	105	153	226
6	370	0.33	0.2	66	70	88	90	94
7	570	0.13	0.6	67	104	134	197	266
8	570	0.23	0.2	58	68	104	149	195
9	570	0.33	1.0	53	79	100	144	171

试验序号	s₁	s₂	s₃	s
1	1.000	1.000	1	1.0000
2	1.000	1.769	3	0.9213
3	1.000	2.538	5	0.8521
4	2.176	1.000	3	1.5900
5	2.176	1.769	5	1.3470
6	2.176	2.538	1	0.9206
7	3.350	1.000	3	1.8860
8	3.350	1.769	1	1.2700
9	3.350	2.538	5	1.3740

项目	初始估计	更新的估计
b₁	0.501 60	0.3947
b₂	-0.548 80	-0.4183
b₃	0.104 10	0.1427
a	34.400 00	38.6000
b	0.212 90	0.1155
c	0.025 78	0.0337
σ	1.257 00	1.1347
ln（L）	-177.454 00	-172.9840

项目	a₀	a₁	a₂	a₃	a₄
系数值	0.6871	0.3171	-0.3869	0.1112	0.6033
p值	0.0307	0.0000	0.0000	0.0033	0.0000

项目	本文模型		回归模型
项目	ε_A	ε_max	ε_A	ε_max
t=5	0.1431	0.2422	0.1618	0.5013
t=10	0.0817	0.1454	0.1066	0.2279
t=15	0.0451	0.0904	0.0846	0.1545
t=20	0.0586	0.1288	0.0670	0.1135
t=25	0.1159	0.2537	0.1751	0.4157
SSR/N	165.5	-	363.8	-
k	6	-	5	-
AIC	241.9	-	275.3	-